There are many definitions of metamaterials, which highlight various aspects of this concept.

Metamaterial is an arrangement of artificial structural elements, designed to achieve advantageous and unusual electromagnetic properties.

Even such a flexible definition is incomplete on the one hand, and too strict, on the other. It is helpful to draw the following analogy: Metamaterial is composed of its elements in the same sense as matter consists of atoms. But these structural elements themselves are made of conventional materials, i.e., finally, of normal atoms. Accordingly, metamaterial represents the next level of structural organization of matter.

Detailed discussions of the metamaterial concept can be found, for example, in following reviews:

The concept of material implies homogeneity, and, if a metamaterial is a periodical structure, the lattice constants should be considerably smaller than the wavelength. This distinguishes metamaterials from photonic (electromagnetic) crystals and frequency-selective surfaces, whose useful and unusual electromagnetic properties originate from the periodicity of their structure. In contrast to photonic crystals, metamaterials can be realized as random mixtures of "artificial molecules".

Metamaterials are often associated with negative refraction, although this is only one of the possible unusual electromagnetic phenomena. Large collection of historical references on that subject is offered on the webpage of Alexander Moroz.